You can put this solution on YOUR website! Rearrange until you get it into slope-intercept form: y = mx+b.
.
(-2/3)x+5=x+y-3
.
Multiply everything by 3...
.
3((-2/3)x+5)=3(x+y-3)
-2x + 15 = 3x + 3y - 9
.
Subtract 3x from both sides...
.
-5x + 15 = 3y -9
.
Add 9 to both sides...
.
-5x + 24 = 3y
.
Divide both sides by 3...
.
(-5/3)x + 8 = y
.
y = (-5/3)x + 8
.
slope = -5/3
y-intercept occurs where x=0, which is...
y = (-5/3)(0) + 8 = 8
or the point (0,8).
.
You only need two points to draw a straight line, so the x-intercept is useful.
It occurs where y=0.
.
0 = (-5/3)x + 8
.
Multiply by 3
0 = -5x + 24
.
Add 5x to both sides
5x = 24
.
Divide by 5
.
x = 24/5 = 4+4/5 = 4.80
which is the point (4.8,0)
.
You can check the graph to see...
.
(